Q. 133.6( 15 Votes )

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Answer :

Proof


Let ABC be a triangle,


Now,


< +___________________ (i)


< +___________________ (ii)


< +___________________ (iii)


2 < ++ [From equation (i)]


2 < 180° [Sum of angles of triangle]


< 90° ________________ (a)


Similarly,


< 90°__________________ (b)


< 90°__________________ (c)


From equation (a), (b) and (c), each angle is less than 90°


Therefore triangle is an acute angled Proved.


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